{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XSKN4HUKF5XY3YCFU6GLPL76D4","short_pith_number":"pith:XSKN4HUK","schema_version":"1.0","canonical_sha256":"bc94de1e8a2f6f8de045a78cb7affe1f2aa1d45c3b92568027ad5a98bedc3670","source":{"kind":"arxiv","id":"1601.05133","version":1},"attestation_state":"computed","paper":{"title":"Generalized Brotbek's symmetric differential forms and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Song-Yan Xie","submitted_at":"2016-01-19T23:33:43Z","abstract_excerpt":"Over an algebraically closed field $\\mathbb{K}$ with any characteristic, on an $N$-dimensional smooth projective $\\mathbb{K}$-variety $\\mathbf{P}$ equipped with $c\\geqslant N/2$ very ample line bundles $\\mathcal{L}_1,\\dots,\\mathcal{L}_c$, we study the General Debarre Ampleness Conjecture, which expects that for all large degrees $d_1,\\dots,d_c\\geqslant d_0\\gg 1$, for generic $c$ hypersurfaces $\nH_1\\in \\big|\\mathcal{L}_1^{\\,\\otimes\\,d_1}\\big|$, $\\dots$, $H_c\\in \\big|\\mathcal{L}_c^{\\,\\otimes\\,d_c}\\big|$, the complete intersection $X:=H_1 \\cap \\cdots \\cap H_c$ has ample cotangent bundle $\\Omega_X"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1601.05133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-19T23:33:43Z","cross_cats_sorted":[],"title_canon_sha256":"b9cdecb8abbc7d885d9444268e0ca1e8b90a706cd35c4c7d450bc646ddf403f3","abstract_canon_sha256":"058183173e5d7e328108418847d1e54ce01176c73746b556d996504cb01b793f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:16.039962Z","signature_b64":"r8oO6vDp6Wl86gMlUrtYONwP1bEqCJvGq112yvhZPhb2I/Yd6XW6VTGf6lswA37Zm+6rK8igzo6vXfks4xzYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc94de1e8a2f6f8de045a78cb7affe1f2aa1d45c3b92568027ad5a98bedc3670","last_reissued_at":"2026-05-18T01:22:16.039376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:16.039376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Brotbek's symmetric differential forms and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Song-Yan Xie","submitted_at":"2016-01-19T23:33:43Z","abstract_excerpt":"Over an algebraically closed field $\\mathbb{K}$ with any characteristic, on an $N$-dimensional smooth projective $\\mathbb{K}$-variety $\\mathbf{P}$ equipped with $c\\geqslant N/2$ very ample line bundles $\\mathcal{L}_1,\\dots,\\mathcal{L}_c$, we study the General Debarre Ampleness Conjecture, which expects that for all large degrees $d_1,\\dots,d_c\\geqslant d_0\\gg 1$, for generic $c$ hypersurfaces $\nH_1\\in \\big|\\mathcal{L}_1^{\\,\\otimes\\,d_1}\\big|$, $\\dots$, $H_c\\in \\big|\\mathcal{L}_c^{\\,\\otimes\\,d_c}\\big|$, the complete intersection $X:=H_1 \\cap \\cdots \\cap H_c$ has ample cotangent bundle $\\Omega_X"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05133","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1601.05133","created_at":"2026-05-18T01:22:16.039449+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.05133v1","created_at":"2026-05-18T01:22:16.039449+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05133","created_at":"2026-05-18T01:22:16.039449+00:00"},{"alias_kind":"pith_short_12","alias_value":"XSKN4HUKF5XY","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XSKN4HUKF5XY3YCF","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XSKN4HUK","created_at":"2026-05-18T12:30:51.357362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XSKN4HUKF5XY3YCFU6GLPL76D4","json":"https://pith.science/pith/XSKN4HUKF5XY3YCFU6GLPL76D4.json","graph_json":"https://pith.science/api/pith-number/XSKN4HUKF5XY3YCFU6GLPL76D4/graph.json","events_json":"https://pith.science/api/pith-number/XSKN4HUKF5XY3YCFU6GLPL76D4/events.json","paper":"https://pith.science/paper/XSKN4HUK"},"agent_actions":{"view_html":"https://pith.science/pith/XSKN4HUKF5XY3YCFU6GLPL76D4","download_json":"https://pith.science/pith/XSKN4HUKF5XY3YCFU6GLPL76D4.json","view_paper":"https://pith.science/paper/XSKN4HUK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.05133&json=true","fetch_graph":"https://pith.science/api/pith-number/XSKN4HUKF5XY3YCFU6GLPL76D4/graph.json","fetch_events":"https://pith.science/api/pith-number/XSKN4HUKF5XY3YCFU6GLPL76D4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XSKN4HUKF5XY3YCFU6GLPL76D4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XSKN4HUKF5XY3YCFU6GLPL76D4/action/storage_attestation","attest_author":"https://pith.science/pith/XSKN4HUKF5XY3YCFU6GLPL76D4/action/author_attestation","sign_citation":"https://pith.science/pith/XSKN4HUKF5XY3YCFU6GLPL76D4/action/citation_signature","submit_replication":"https://pith.science/pith/XSKN4HUKF5XY3YCFU6GLPL76D4/action/replication_record"}},"created_at":"2026-05-18T01:22:16.039449+00:00","updated_at":"2026-05-18T01:22:16.039449+00:00"}